My time will soon be over. I shall have to say good-bye and leave. I came to the Earth when the world was still peaceful. It was the time when people believed in the infinite future, when the Russian Empire was still flourishing. I had an active life: I worked a lot, I stood up against many things, I had friends and teachers, I passed through the circle of suffering beyond Dante's imagination, I wrote many books that were edited either (...) in our country or at least in the West. Now I feel like looking around and trying to comprehend what has happened, what I participated in, what was it that people who were my kin perished for? What are we leaving to the future inhabitants of the Earth? I am well aware of living at the turning point of culture. But what can be said about that? And who will hear what we say? (shrink)

In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical (...) language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case. (shrink)

“For there shall be days when you will say: Blessed is the womb which has not conceived, and those breasts which have not given suck.”The Apocryphal Gospel of Thomas (1)“ Oh man! why is the world becoming so narrow for you? You want to possess it alone; but if you had possessed it, it would not have been spacious enough for you:Ah! this is the pride of the devil who has fallen from heaven into hell.”.

The attention of scientists is now being drawn to a new branch of knowledge known as the “philosophy of science.” It is true, however, that philosophers of this country are not very happy about this word combination and often identify it with logical, positivism. Indeed, it would seem better to speak not of the philosophy, but of the logic of scientific development. Science has become an object of study, and there has emerged metascience, i.e., a science studying the logic of (...) scientific structures. This field of knowledge cannot so far boast of generally accepted results. But it has done something else: new acute questions have been formulated and discussed fruitfully and originally. With this paper we are making an attempt to enter the discussion. The philosophy of science has not certainly taught scientists to discover the truth but it has indubitably increased their criticism towards their own activities, and this is really a very important accomplishment. (shrink)